The coefficient of volume expansion of glycerine is 49 × 10 - 5 K - 1 . The fractional change in its density for a 30 ° C rise in temperature will be

Step-by-step solution

Let V 0 be the initial volume of glycerine, i.e, at 0 ° C (dry). If V t be its volume at 30 ° C Then V t = V 0 1 + v ∆ t = V 0 1 + 49 × 10 - 5 × 30 V t = V 0 1 + 0.01470 = 1.0147070 V 0 ⇒ V 0 V t = 1 1.01470 Let ρ o and ρ t be the initial and final densities of glycertine then initial density, ρ 0 = m v 0 and final density, ρ t = m V t Where, m = mass of glycertine ∆ ρ ρ 0 = fractional change in the density ρ t - ρ 0 ρ 0 = m 1 V t - 1 V 0 m V 0 = V 0 V t - 1 ∆ ρ ρ 0 = 1 1.01470 - 1 = - 0.0145 Here, negative sign sh